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IIT JEE Advanced 2009 Paper 1
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© examsnet.com
Question : 51
Total: 60
Let L =
lim
x
→
0
a
−
√
a
2
−
x
2
−
x
2
4
x
4
, a > 0. If L is finite, then
a = 2
a = 1
L =
1
64
L =
1
32
Validate
Solution:
The given limit is
L =
lim
x
→
0
a
−
√
a
2
−
x
2
−
x
2
4
x
4
=
lim
x
→
0
1
x
2
(
a
+
√
a
2
−
x
2
)
*
1
4
x
2
=
lim
x
→
0
(
4
−
a
)
−
√
a
2
−
x
2
4
x
2
(
a
+
√
a
2
−
x
2
)
The numerator → 0 if a = 2; therefore, L =
1
64
© examsnet.com
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